For example the EQ loudness in my Wiim is boosting lower frequencies and boosts a bit the higher frequencies. Can those boosted lower frequencies just increase distortion at the speaker? What is the measurement to show us that?
Absolutely. If you boost low frequencies inappropriately, you WILL increase distortion. I picked a speaker at random from Amir's review database, but let us look at the
Polk Audio Signature S15 as an example of a small speaker which is deficient in bass frequencies. This is Amir's measured FR:
OK so we see that bass drops off sharply at 90Hz. It is 85dB at 90Hz, and 73dB at 45Hz ... i.e. a drop of 12dB/octave. Can this be boosted with EQ? Let's look at his distortion measurements:
We see that distortion goes off the scale <70Hz, even at 86dB. At 96dB it is even worse. So: this speaker is NOT a candidate for bass boost.
You could look at other speakers to see how they would perform, but in general - your bass boost is limited by onset of audible distortion. The actual limit depends on you, because you may be able to tolerate more audible distortion than other people. Some people hate the idea of distortion and set their limits lower so that nothing ever distorts. And let's face it, this is not a mission critical application of audio here. You are not a submarine sonar operator where life or death depends on clean signal
So for me, I tolerate some distortion because to get rid of it requires purchase of more equipment.
You can perform your own distortion measurements. You need a microphone, a PC, REW, an SPL meter, and a microphone tripod. The "standard" method is: place your mic 1m away from the speaker and play a 1kHz test tone. Adjust the volume of the tone so that it is 86dB, and adjust the gain on the mic in REW so that it reads 86dB. However, room reflections will affect your distortion measurements, so there is a lower limit where these will be meaningful, and it will not capture bass distortion. So I suggest placing your mic even closer, i.e. almost touching the speaker. You might have to measure driver and port separately. Then perform a sweep, and click on the "distortion" tab. You will see a trace similar to Amir's. Repeat the test at 96dB and as loud as the speaker will go (wear hearing protection!).